Grade 5 Pre-Algebra Worksheet: Solve for the variable x.

Let's solve each of the 20 basic algebra equations from the worksheet step by step. The goal is to solve for the variable $ x $ in each equation, and express the answer as "$ x = $" (e.g., $ x = 5 $).

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1) $ x + 12 = 14 $

Subtract 12 from both sides:
$ x = 14 - 12 $
$ x = 2 $

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2) $ 11 + x = 15 $

Subtract 11 from both sides:
$ x = 15 - 11 $
$ x = 4 $

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3) $ x - 5 = 6 $

Add 5 to both sides:
$ x = 6 + 5 $
$ x = 11 $

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4) $ 2 + x = 8 $

Subtract 2 from both sides:
$ x = 8 - 2 $
$ x = 6 $

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5) $ x - 3 = 2 $

Add 3 to both sides:
$ x = 2 + 3 $
$ x = 5 $

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6) $ x - 6 = 6 $

Add 6 to both sides:
$ x = 6 + 6 $
$ x = 12 $

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7) $ 7 + x = 14 $

Subtract 7 from both sides:
$ x = 14 - 7 $
$ x = 7 $

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8) $ 12 - x = 7 $

Subtract 12 from both sides:
$ -x = 7 - 12 $
$ -x = -5 $
Multiply both sides by -1:
$ x = 5 $

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9) $ 5 + x = 9 $

Subtract 5 from both sides:
$ x = 9 - 5 $
$ x = 4 $

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10) $ x - 10 = 2 $

Add 10 to both sides:
$ x = 2 + 10 $
$ x = 12 $

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11) $ x + 6 = 14 $

Subtract 6 from both sides:
$ x = 14 - 6 $
$ x = 8 $

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12) $ 7 + x = 10 $

Subtract 7 from both sides:
$ x = 10 - 7 $
$ x = 3 $

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13) $ 10 - x = 7 $

Subtract 10 from both sides:
$ -x = 7 - 10 $
$ -x = -3 $
Multiply both sides by -1:
$ x = 3 $

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14) $ 8 + x = 15 $

Subtract 8 from both sides:
$ x = 15 - 8 $
$ x = 7 $

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15) $ 8 - x = 1 $

Subtract 8 from both sides:
$ -x = 1 - 8 $
$ -x = -7 $
Multiply both sides by -1:
$ x = 7 $

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16) $ x + 10 = 14 $

Subtract 10 from both sides:
$ x = 14 - 10 $
$ x = 4 $

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17) $ x - 3 = 8 $

Add 3 to both sides:
$ x = 8 + 3 $
$ x = 11 $

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18) $ x + 7 = 9 $

Subtract 7 from both sides:
$ x = 9 - 7 $
$ x = 2 $

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19) $ x + 7 = 19 $

Subtract 7 from both sides:
$ x = 19 - 7 $
$ x = 12 $

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20) $ x + 2 = 10 $

Subtract 2 from both sides:
$ x = 10 - 2 $
$ x = 8 $

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✔ Final Answers:

1) $ x = 2 $
2) $ x = 4 $
3) $ x = 11 $
4) $ x = 6 $
5) $ x = 5 $
6) $ x = 12 $
7) $ x = 7 $
8) $ x = 5 $
9) $ x = 4 $
10) $ x = 12 $
11) $ x = 8 $
12) $ x = 3 $
13) $ x = 3 $
14) $ x = 7 $
15) $ x = 7 $
16) $ x = 4 $
17) $ x = 11 $
18) $ x = 2 $
19) $ x = 12 $
20) $ x = 8 $

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🔍 Explanation:

These are all one-step linear equations, meaning you only need one operation (addition, subtraction, etc.) to isolate the variable $ x $. The key steps are:
- If $ x $ is being added to a number, subtract that number from both sides.
- If $ x $ is being subtracted from a number, add that number to both sides.
- Always keep the equation balanced by doing the same operation on both sides.

This builds foundational algebra skills for solving more complex equations later.

Let me know if you'd like this formatted as a printable answer sheet!